There are a few REALLY big skill gaming sites, along with plenty more to take advantage of with the largest having 50K+ people online at a time. The largest is StarGames.com featuring Free games, Huge site, Lots of ways to compete, many tournaments and much more.

The list of games is endless but here's a few examples:
Backgammon, Belote, Blackjack, Hearts, Rummy, Minesweeper, Darts, Mah Jong, Scrabble, Sudoku, Zuma, Pool, Solitaire, Pyramid, Spades, Gin, Cantasia, Bejeweled and a whole lot more!

Most Skill Gaming sites do Head to Head battles, You each pay a entry fee, most sites have tourneys starting at under a dollar. You two play the same game, with the same game conditions, the higher score wins the money. Most Sites also offer larger Jackpot tourneys sometimes above €10,000, where any number of people can play and the tourney ends on a given date/time. Everyone pays the same entry fee and it goes into a prize pool which is split amongst the top finishers for the tourney. Again everyone plays the same game with same conditions so everyone has a level playing field. Most of these tourneys also have a buy-in starting at a Euro with larger buy-in tourneys once you get more experienced. Usually a top 3 finish in these types of tourneys get's you a nice three digit pay day.

All sites have a minimum deposit and minimum withdraw amount so they aren't doing 100's of 75 cent transfers. This is usually €10. Some also offer credit card, money transfers and other online payment processors for funding and withdraws.

Most sites have a free play option so you can learn the game, practice and get better with out risking anything. Some will even give you some free money to play with, but will require a deposit before they let you cash out the free money.

You can easily play with 100's of games with a single €20 deposit on most sites if you spend just a little time practicing.